Calculate Min Speed of Electron from Neutron Star in Nebula

[JTraik]

Homework Statement

The following is the problem at hand. I am having difficulty starting out because I do not understand what is going to happen, in a general sense.

You have landed a summer job working with an Astrophysics group investigating the origin of high-energy particles in the galaxy. The group you are joining has just discovered a large spherical nebula with a radius 1.2 million km. The nebula consists of about 5 x 10E10 hydrogen nuclei (protons) which appear to be uniformly distributed in the shape of a sphere. At the center of this sphere of positive charge is a very small neutron star. Your group had detected electrons emerging from the nebula. A friend of yours has a theory that the electrons are coming from the neutron star. To test that theory, she asks you to calculate the minimum speed that an electron would need to start from the neutron star and just make it to outside the nebula. From the inside cover of your trusty physics text you find that the charge of a proton (and an electron) is 1.6 x 10E-19 C, the mass of the proton is 1.7 x 10E-27 kg, and the mass of the electron is 9.1 x 10E-31 kg.

Homework Equations

I am confused on how an electron would behave in a field of protons and also vica versa. Since the electric field inside a conductor is zero, what is repelling and attracting this electron, shouldn't it just float freely around inside the "nebula"? I am assuming electric potential plays the role here, however it is submerged (no distance between) in a field, how can there be potential?

Your assistance is most appreciated, thank you!

 

[Gokul43201]

Recall any similar problems you may have solved in an intro E&M course (think Gauss' Law).

 

[dynamicsolo]

If I'm reading the intent of this problem right, this nebula is not to be treated as a conductor, but as an (ideal) insulating sphere with a fixed, uniformly-dense, positive charge distribution (the density is really low!). I am assuming that the bit with the neutron star is that the very center of the sphere is neutral (and so tiny compared to the spherical nebula that its size can be neglected). [Never mind that this "nebula" makes little sense in terms of physical stability...] I'm also assuming we can ignore gravitational effects for climbing away from the neutron star (which is also a little silly).

So, as Gokul43201 says, you want to use what you've learned from Gauss' Law to find the behavior of the field within the nebula. (It may also be worthwhile to use that result to find the potential energy change between the endpoints of the electron's path to the surface.)